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On the number of periodic reflecting rays in generic domains. (English) Zbl 0668.58005

Authors’ abstract: We prove that for generic domains \(\Omega \subset {\mathbb{R}}^ n\) with smooth boundary X for every integer \(s\geq 2\) there is at most a finite number of periodic reflecting rays with just s reflections on X.
Reviewer: J.Mihut

MSC:

58A99 General theory of differentiable manifolds
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References:

[1] Katok, Lecture Notes in Mathematics 1222 (1986)
[2] Katok, Ergod. Th. & Dynam. Sys. 2 pp 339– (1982)
[3] Golubitsky, Stable Mappings and their Singularities (1973) · doi:10.1007/978-1-4615-7904-5
[4] Stojanov, C.R. Acad. Bulgare Sci. 39 pp 13– (1986)
[5] Stojanov, Ergod. Th. Dynam. Sys. 7 pp none– (1987)
[6] DOI: 10.1007/BF01076325 · Zbl 0207.20305 · doi:10.1007/BF01076325
[7] DOI: 10.2307/2374608 · Zbl 0652.35027 · doi:10.2307/2374608
[8] DOI: 10.1080/03605308008820141 · Zbl 0435.35065 · doi:10.1080/03605308008820141
[9] DOI: 10.1007/BF01161919 · Zbl 0673.58035 · doi:10.1007/BF01161919
[10] DOI: 10.1002/cpa.3160310504 · Zbl 0368.35020 · doi:10.1002/cpa.3160310504
[11] DOI: 10.1090/S0273-0979-1986-15445-5 · Zbl 0602.58050 · doi:10.1090/S0273-0979-1986-15445-5
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